IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v91y2016icp319-328.html
   My bibliography  Save this article

The concept of fractal experiments: New possibilities in quantitative description of quasi-reproducible measurements

Author

Listed:
  • Nigmatullin, R.R.
  • Evdokimov, Yu.K.

Abstract

In this paper the authors suggest a new conception of the so-called fractal (self-similar) experiment. Under the fractal experiment (FE) one can imply a cycle of measurements that are subjected by the scaling transformations F(z)→F(zξm) in contrast with conventional scheme F(z)→F(z+mT) (m=0,1,…, M–1), where z defines the controllable (input) variable and can be associated with time, complex frequency, wavelength and etc., T – mean period of time between successive measurements and m defines a number of successive measurements. One can connect a fractal experiment with specific memory effect that arises between successive measurements. The general theory of experiment for quasi-periodic measurements proposed in [1] after some transformations can be applied for the set of the FE, as well. But attentive analysis shown in this paper allows generalizing the previous results for the case when the influence of uncontrollable factors becomes significant. The theory developed for this case allows to consider more real cases when the influence of dynamic (unstable) processes taking place during the cycle of measurements corresponding to some FE is becoming essential. These experiments we define as quasi-reproducible (QR) fractal experiments.

Suggested Citation

  • Nigmatullin, R.R. & Evdokimov, Yu.K., 2016. "The concept of fractal experiments: New possibilities in quantitative description of quasi-reproducible measurements," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 319-328.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:319-328
    DOI: 10.1016/j.chaos.2016.06.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916302107
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.06.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hilfer, R., 1995. "An extension of the dynamical foundation for the statistical equilibrium concept," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 89-96.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nigmatullin, R.R. & Budnikov, H.C. & Sidelnikov, A.V., 2018. "Mesoscopic theory of percolation currents associated with quantitative description of VAGs: Confirmation on real data," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 171-183.
    2. Nigmatullin, Raoul & Sarkar, Samyadip & Biswas, Karabi, 2021. "New class of fractal elements with log-periodic corrections: Confirmation on experimental data," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. R. Hilfer, 2015. "Time Automorphisms on C*-Algebras," Mathematics, MDPI, vol. 3(3), pages 1-18, July.
    2. Ram K. Saxena & Zivorad Tomovski & Trifce Sandev, 2015. "Analytical Solution of Generalized Space-Time Fractional Cable Equation," Mathematics, MDPI, vol. 3(2), pages 1-18, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:319-328. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.